Exclude old man on the rise (4)
I believe the answer is:
omit
'exclude' is the definition.
(I know that exclude can be written as omit)
'old man on the rise' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'man' becomes 'tim' (short for Timothy).
'on the rise' is a reversal indicator (in a down clue, letters go up).
'tim' in reverse letter order is 'mit'.
'o'+'mit'='OMIT'
(Other definitions for omit that I've seen before include "Skip" , "Leave out or overlook" , "Leave out or neglect" , "Neglect to include" , "Fail to mention" .)